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Click [link] for a more complete list of conversion factors.
Lengths in meters | Masses in kilograms (more precise values in parentheses) | Times in seconds (more precise values in parentheses) | |||
---|---|---|---|---|---|
${\text{10}}^{-\text{18}}$ | Present experimental limit to smallest observable detail | $${\text{10}}^{-\text{30}}$$ | Mass of an electron $\left(9\text{.}\text{11}\times {\text{10}}^{-\text{31}}\phantom{\rule{0.25em}{0ex}}\text{kg}\right)$ | $${\text{10}}^{-\text{23}}$$ | Time for light to cross a proton |
$${\text{10}}^{-\text{15}}$$ | Diameter of a proton | $${\text{10}}^{-\text{27}}$$ | Mass of a hydrogen atom $\left(1\text{.}\text{67}\times {\text{10}}^{-\text{27}}\phantom{\rule{0.25em}{0ex}}\text{kg}\right)$ | $${\text{10}}^{-\text{22}}$$ | Mean life of an extremely unstable nucleus |
$${\text{10}}^{-\text{14}}$$ | Diameter of a uranium nucleus | $${\text{10}}^{-\text{15}}$$ | Mass of a bacterium | $${\text{10}}^{-\text{15}}$$ | Time for one oscillation of visible light |
$${\text{10}}^{-\text{10}}$$ | Diameter of a hydrogen atom | $${\text{10}}^{-5}$$ | Mass of a mosquito | $${\text{10}}^{-\text{13}}$$ | Time for one vibration of an atom in a solid |
$${\text{10}}^{-8}$$ | Thickness of membranes in cells of living organisms | $${\text{10}}^{-2}$$ | Mass of a hummingbird | $${\text{10}}^{-8}$$ | Time for one oscillation of an FM radio wave |
$${\text{10}}^{-6}$$ | Wavelength of visible light | $$\text{1}$$ | Mass of a liter of water (about a quart) | $${\text{10}}^{-3}$$ | Duration of a nerve impulse |
$${\text{10}}^{-3}$$ | Size of a grain of sand | $${\text{10}}^{2}$$ | Mass of a person | $$\text{1}$$ | Time for one heartbeat |
$$\text{1}$$ | Height of a 4-year-old child | $${\text{10}}^{3}$$ | Mass of a car | $${\text{10}}^{5}$$ | One day $\left(8\text{.}\text{64}\times {\text{10}}^{4}\phantom{\rule{0.25em}{0ex}}\text{s}\right)$ |
$${\text{10}}^{2}$$ | Length of a football field | $${\text{10}}^{8}$$ | Mass of a large ship | $${\text{10}}^{7}$$ | One year (y) $\left(3\text{.}\text{16}\times {\text{10}}^{7}\phantom{\rule{0.25em}{0ex}}\text{s}\right)$ |
$${\text{10}}^{4}$$ | Greatest ocean depth | $${\text{10}}^{\text{12}}$$ | Mass of a large iceberg | $${\text{10}}^{9}$$ | About half the life expectancy of a human |
$${\text{10}}^{7}$$ | Diameter of the Earth | $${\text{10}}^{\text{15}}$$ | Mass of the nucleus of a comet | $${\text{10}}^{\text{11}}$$ | Recorded history |
$${\text{10}}^{\text{11}}$$ | Distance from the Earth to the Sun | $${\text{10}}^{\text{23}}$$ | Mass of the Moon $\left(7\text{.}\text{35}\times {\text{10}}^{\text{22}}\phantom{\rule{0.25em}{0ex}}\text{kg}\right)$ | $${\text{10}}^{\text{17}}$$ | Age of the Earth |
$${\text{10}}^{\text{16}}$$ | Distance traveled by light in 1 year (a light year) | $${\text{10}}^{\text{25}}$$ | Mass of the Earth $\left(5\text{.}\text{97}\times {\text{10}}^{\text{24}}\phantom{\rule{0.25em}{0ex}}\text{kg}\right)$ | $${\text{10}}^{\text{18}}$$ | Age of the universe |
$${\text{10}}^{\text{21}}$$ | Diameter of the Milky Way galaxy | $${\text{10}}^{\text{30}}$$ | Mass of the Sun $\left(1\text{.}\text{99}\times {\text{10}}^{\text{30}}\phantom{\rule{0.25em}{0ex}}\text{kg}\right)$ | ||
$${\text{10}}^{\text{22}}$$ | Distance from the Earth to the nearest large galaxy (Andromeda) | $${\text{10}}^{\text{42}}$$ | Mass of the Milky Way galaxy (current upper limit) | ||
$${\text{10}}^{\text{26}}$$ | Distance from the Earth to the edges of the known universe | $${\text{10}}^{\text{53}}$$ | Mass of the known universe (current upper limit) |
Suppose that you drive the 10.0 km from your university to home in 20.0 min. Calculate your average speed (a) in kilometers per hour (km/h) and (b) in meters per second (m/s). (Note: Average speed is distance traveled divided by time of travel.)
Strategy
First we calculate the average speed using the given units. Then we can get the average speed into the desired units by picking the correct conversion factor and multiplying by it. The correct conversion factor is the one that cancels the unwanted unit and leaves the desired unit in its place.
Solution for (a)
(1) Calculate average speed. Average speed is distance traveled divided by time of travel. (Take this definition as a given for now—average speed and other motion concepts will be covered in a later module.) In equation form,
(2) Substitute the given values for distance and time.
(3) Convert km/min to km/h: multiply by the conversion factor that will cancel minutes and leave hours. That conversion factor is $\text{60 min/hr}$ . Thus,
Discussion for (a)
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